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Unformatted text preview: ECES302 Sample Endterm: Total = ............../40 A grade out of 20 for the computer explorations portion of this course will be calculated as 40% endterm + 60% weekly work. Then any bonus points will be added. Each question on the computer endterm is graded out of 5. Here are 14 typical questions. Your test will have only 8. For each problem you can use your choice of Maple or Matlab unless otherwise specified. Be sure to open a new window for each question before you close the old one. Do not do more than one problem in the same Maple worksheet or Matlab mfile. "Show for credit" exercises will not receive part marks. Exercise 1  a. Find the exact form of the number y = j (1+j) . 1a. y = ………….. + ………………. j (2) b. Evaluate it to 30 digits and write down the last digit. 1b. Last digit of y = ……………………..….. (2) c. Compute the product p = (1+2j) (2+3j) 1c. p = ………….. + ………………. j (1) Exercise 2  a. Plot the piecewise function x(t) shown after defining u(t) and r(t). In Matlab, u.m and r.m will be provided. In Maple you will need to define them using the arrow notation. (3) Hint: x(t) = 3 r(t+2)  6 r(t+1) + 3r(t) + 3 u(t)  3 u(t2) b. Find the integral of x ( t ) from – ∞ to + ∞ using the int command. (2) 2a. Show for Credit ......……........... 2b. Integral = ....…….............. Exercise 3  a. Plot the even component of the function x ( t ) = e – t u ( t ) (3) 3a. Show for Credit ......……........... b. Create a simultaneous plot of the even and odd components in red and green respectively. (2) 3b. Show for Credit ......……........... Exercise 4  Periodic Extensions of Piecewise Functions (See Lab 5) a. Assume the parabolic function y = t – t 2 is periodically extended using its values from 0 to 1 as the first period. Obtain a plot of this periodic extension. (3) Hint: Saw := t > tfloor(t): T0 := 1: P := t > T0*Saw(t/T0): yp := t > y(P(t)); 4a. Show for Credit ......................
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 Spring '08
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